We investigate the many-particle and mean-field correspondence for a non-Hermitian N-
particle Bose-Hubbard dimer where a complex on-site energy describes an effective decay …

In this paper, we consider the following algebraic hypersurfaces S 1× S 2={(x 1, x 2, x 3, x
4)∈ R 4:(x 1 2+ x 2 2− a 2) 2+ x 3 2+ x 4 2− 1= 0 and a> 1} and S 2× S 1={(x 1, x 2, x 3, x …

We investigate an open Bose–Hubbard dimer with a non-Hermitian term represents an
asymmetric coupling between the two sites. By mapping to the collective angular moment …

In this paper, we consider the following two algebraic hypersurfaces $$ S^ 1\times S^
2=\{(x_1, x_2, x_3, x_4)\in\mathbb {R}^ 4:(x_1^ 2+ x_2^ 2-a^ 2)^ 2+ x_3^ 2+ x_4^ 2-1= 0; …

We present some necessary conditions for quasi-homogeneous differential systems to be
completely integrable via Kovalevskaya exponents. Then, as an application, we give a new …

Let X be a homogeneous polynomial vector field of degree 2 on S^ 2. We show that if X has
at least a non-hyperbolic singularity, then it has no limit cycles. We give necessary and …

We extend to the $ n $-dimensional ellipsoid contained in $\R^{n+ 1}, $ the Darboux theory
of integrability for polynomial vector fields in the $ n $-dimensional sphere (Llibre et al …

In this paper, we characterize arbitrary polynomial vector fields on $ S^ n $. We establish a
necessary and sufficient condition for a degree one vector field on the odd-dimensional …

In this paper, we characterize and study dynamical properties of cubic vector fields on the
sphere S 2={(x, y, z)∈ R 3| x 2+ y 2+ z 2= 1}. We start by classifying all degree three …

A class of reversible quadratic polynomial vector fields on S2 Page 1 J. Math. Anal. Appl. 371
(2010) 203–209 Contents lists available at ScienceDirect Journal of Mathematical Analysis …